Realization of the annihilation operator for generalized oscillator-like system by a differential operator

Details Realization of the annihilation operator for generalized oscillator-like system by a differential operator Realization of the annihilation operator for generalized oscillator-like system by a differential operator

2001-01-25

arxiv.org/abs/math/0101215v1

Mathematics

Quantum Algebra

13 pages, no figures

Scientific paper

This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential operator A is obtained. The important special case of orthogonal polynomial systems, for which the matrix of the operator A in $l^2(Z_+)$ has only off-diagonal elements on the first upper diagonal different from zero, is considered. The known generalized Hermite polynomials give us an example of such orthonormal system. The replacement of the usual derivative by q-derivative allows us to use the suggested approach for similar investigation of various "deformed" polynomials.

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